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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
180.1.f.a \(2\) \(0.090\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{15}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}-iq^{5}+iq^{8}-q^{10}+\cdots\)
180.1.m.a \(4\) \(0.090\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}-\zeta_{8}q^{8}+\cdots\)
180.1.p.a \(2\) \(0.090\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-5}) \) None \(-1\) \(-1\) \(-1\) \(1\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
180.1.p.b \(2\) \(0.090\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-5}) \) None \(1\) \(1\) \(-1\) \(-1\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
180.2.a.a \(1\) \(1.437\) \(\Q\) None None \(0\) \(0\) \(1\) \(2\) \(-\) \(q+q^{5}+2q^{7}+2q^{13}+6q^{17}-4q^{19}+\cdots\)
180.2.d.a \(2\) \(1.437\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) \(q+(-1+i)q^{5}+2iq^{7}+4q^{11}-2iq^{17}+\cdots\)
180.2.e.a \(8\) \(1.437\) 8.0.18939904.2 None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{2}+\beta _{6})q^{2}+(\beta _{4}-\beta _{5}+\beta _{7})q^{4}+\cdots\)
180.2.h.a \(4\) \(1.437\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}+2q^{4}-\zeta_{8}^{2}q^{5}+2\zeta_{8}^{3}q^{8}+\cdots\)
180.2.h.b \(8\) \(1.437\) 8.0.3317760000.1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+\beta _{3}q^{4}+(-\beta _{2}-\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\)
180.2.i.a \(2\) \(1.437\) \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(-1\) \(1\) \(q+(2-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
180.2.i.b \(6\) \(1.437\) 6.0.954288.1 None None \(0\) \(-1\) \(3\) \(-3\) \(q-\beta _{1}q^{3}+(1+\beta _{2})q^{5}+(\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
180.2.j.a \(4\) \(1.437\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(8\) \(q+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+(2-2\zeta_{8}^{2})q^{7}+\cdots\)
180.2.k.a \(2\) \(1.437\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(2\) \(0\) \(q+(-1-i)q^{2}+2iq^{4}+(1-2i)q^{5}+\cdots\)
180.2.k.b \(2\) \(1.437\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-2\) \(0\) \(q+(1+i)q^{2}+2iq^{4}+(-1+2i)q^{5}+\cdots\)
180.2.k.c \(2\) \(1.437\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(4\) \(0\) \(q+(1+i)q^{2}+2iq^{4}+(2-i)q^{5}+(-2+\cdots)q^{8}+\cdots\)
180.2.k.d \(8\) \(1.437\) 8.0.157351936.1 None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{2}+\beta _{4})q^{2}+(\beta _{3}+\beta _{5})q^{4}+(2\beta _{4}+\cdots)q^{5}+\cdots\)
180.2.k.e \(12\) \(1.437\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1-\beta _{1}+\beta _{7}+\cdots)q^{5}+\cdots\)
180.2.n.a \(4\) \(1.437\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(-6\) \(6\) \(6\) \(q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
180.2.n.b \(4\) \(1.437\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(6\) \(6\) \(-6\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+(2+\cdots)q^{5}+\cdots\)
180.2.n.c \(8\) \(1.437\) 8.0.3317760000.8 \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}+\beta _{1}q^{3}+2\beta _{3}q^{4}-\beta _{2}q^{5}+\cdots\)
180.2.n.d \(48\) \(1.437\) None None \(0\) \(0\) \(-18\) \(0\)
180.2.q.a \(48\) \(1.437\) None None \(0\) \(0\) \(0\) \(0\)
180.2.r.a \(12\) \(1.437\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(1\) \(0\) \(q+\beta _{1}q^{3}+\beta _{9}q^{5}+(-\beta _{3}+\beta _{6}-\beta _{7}+\cdots)q^{7}+\cdots\)
180.2.w.a \(24\) \(1.437\) None None \(0\) \(-2\) \(0\) \(0\)
180.2.x.a \(128\) \(1.437\) None None \(-2\) \(0\) \(-4\) \(0\)
180.3.b.a \(4\) \(4.905\) \(\Q(\sqrt{-2}, \sqrt{23})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{3})q^{5}-\beta _{2}q^{7}+7\beta _{1}q^{11}+\cdots\)
180.3.c.a \(4\) \(4.905\) \(\Q(\zeta_{10})\) None None \(2\) \(0\) \(0\) \(0\) \(q+\zeta_{10}q^{2}+(-1+\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{4}+\cdots\)
180.3.c.b \(8\) \(4.905\) 8.0.85100625.1 None None \(-4\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}+(1+\beta _{3}+\beta _{4}+\beta _{5})q^{4}+\beta _{3}q^{5}+\cdots\)
180.3.c.c \(8\) \(4.905\) 8.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-2-\beta _{4})q^{4}+\beta _{3}q^{5}+2\beta _{6}q^{7}+\cdots\)
180.3.f.a \(1\) \(4.905\) \(\Q\) \(\Q(\sqrt{-5}) \) None \(-2\) \(0\) \(5\) \(4\) \(q-2q^{2}+4q^{4}+5q^{5}+4q^{7}-8q^{8}+\cdots\)
180.3.f.b \(1\) \(4.905\) \(\Q\) \(\Q(\sqrt{-5}) \) None \(2\) \(0\) \(5\) \(-4\) \(q+2q^{2}+4q^{4}+5q^{5}-4q^{7}+8q^{8}+\cdots\)
180.3.f.c \(2\) \(4.905\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-6\) \(0\) \(q+iq^{2}-4q^{4}+(-3-2i)q^{5}-4iq^{8}+\cdots\)
180.3.f.d \(4\) \(4.905\) \(\Q(\sqrt{-3}, \sqrt{22})\) None None \(-4\) \(0\) \(0\) \(0\) \(q+(-1-\beta _{2})q^{2}+(-2+2\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
180.3.f.e \(4\) \(4.905\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+(2+2\zeta_{12}^{2})q^{4}+\cdots\)
180.3.f.f \(4\) \(4.905\) \(\Q(i, \sqrt{15})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(4+\beta _{3})q^{4}+5\beta _{2}q^{5}+(3\beta _{1}+\cdots)q^{8}+\cdots\)
180.3.f.g \(4\) \(4.905\) \(\Q(\sqrt{-3}, \sqrt{22})\) None None \(4\) \(0\) \(0\) \(0\) \(q+(1+\beta _{2})q^{2}+(-2+2\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
180.3.f.h \(8\) \(4.905\) 8.0.\(\cdots\).4 None None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
180.3.g.a \(4\) \(4.905\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(-16\) \(q-\beta _{2}q^{5}+(-4-\beta _{3})q^{7}+(-\beta _{1}-6\beta _{2}+\cdots)q^{11}+\cdots\)
180.3.l.a \(2\) \(4.905\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(6\) \(-14\) \(q+(3-4i)q^{5}+(-7-7i)q^{7}-10q^{11}+\cdots\)
180.3.l.b \(4\) \(4.905\) \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(-12\) \(20\) \(q+(-3-2\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(5+2\beta _{1}+\cdots)q^{7}+\cdots\)
180.3.l.c \(4\) \(4.905\) \(\Q(i, \sqrt{10})\) None None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{2}q^{5}+(-1-\beta _{1})q^{7}+(3\beta _{2}-\beta _{3})q^{11}+\cdots\)
180.3.m.a \(4\) \(4.905\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2\zeta_{8}q^{2}+4\zeta_{8}^{2}q^{4}+(4\zeta_{8}+3\zeta_{8}^{3})q^{5}+\cdots\)
180.3.m.b \(4\) \(4.905\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2\zeta_{8}q^{2}+4\zeta_{8}^{2}q^{4}+(4\zeta_{8}-3\zeta_{8}^{3})q^{5}+\cdots\)
180.3.m.c \(40\) \(4.905\) None None \(0\) \(0\) \(0\) \(0\)
180.3.o.a \(4\) \(4.905\) \(\Q(\sqrt{-3}, \sqrt{-5})\) None None \(0\) \(-6\) \(0\) \(8\) \(q+(-3+3\beta _{2})q^{3}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
180.3.o.b \(12\) \(4.905\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(2\) \(0\) \(-6\) \(q+\beta _{1}q^{3}+\beta _{8}q^{5}+(\beta _{1}+\beta _{3}-\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots\)
180.3.p.a \(4\) \(4.905\) \(\Q(\sqrt{-3}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) None \(-4\) \(4\) \(10\) \(4\) \(q+(-2+2\beta _{2})q^{2}+(\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+\cdots\)
180.3.p.b \(4\) \(4.905\) \(\Q(\sqrt{-3}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) None \(4\) \(-4\) \(10\) \(-4\) \(q+(2-2\beta _{2})q^{2}+(\beta _{1}-2\beta _{2}-\beta _{3})q^{3}+\cdots\)
180.3.p.c \(128\) \(4.905\) None None \(0\) \(0\) \(-22\) \(0\)
180.3.s.a \(96\) \(4.905\) None None \(0\) \(0\) \(0\) \(0\)
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